pulkit Posted August 13, 2004 Share Posted August 13, 2004 What exactly is variational mechanics and variational calculus ? Link to comment Share on other sites More sharing options...
fuhrerkeebs Posted August 13, 2004 Share Posted August 13, 2004 Variational calculus deals with finding optimal curves and such. Things like geodesics (shortest path). I don't know what you mean by variation mechanics. Link to comment Share on other sites More sharing options...
pulkit Posted August 13, 2004 Author Share Posted August 13, 2004 Variation mechanics : Its a branch of mechanics thats based on variational calculus. All I know is that Lagrange is to variational mechanics what Newton is to classical mechanics. Link to comment Share on other sites More sharing options...
fuhrerkeebs Posted August 13, 2004 Share Posted August 13, 2004 Ah, ok. Well, Langragian mechanics and General relativity both use the shortest path between two points as the path of a particle. Link to comment Share on other sites More sharing options...
pulkit Posted August 13, 2004 Author Share Posted August 13, 2004 Which provides a more accurate description of nature Newtonian or Variational mechanics ? Or is it that they differ only in mathematical terms ? Link to comment Share on other sites More sharing options...
fuhrerkeebs Posted August 13, 2004 Share Posted August 13, 2004 Langragian and Newtonian mechanics differ only in mathematical terms. General relativity differs from Newtonian and Langragian mechanics greatly. Link to comment Share on other sites More sharing options...
Perennial Posted October 30, 2004 Share Posted October 30, 2004 Most of Lagrangian mech applications I do are implemented via energy principles, and actually are pretty identical to principles such as the principle of virtual work or virtual power (equilibrium stuff). I think the mathematical constructs have some added value in comparison to other stuff if you're working for example with dynamics problems or need to include something with similar mathematical aspects, like optimization using numerical methods etc. The math is really elegant, though. Link to comment Share on other sites More sharing options...
Severian Posted November 1, 2004 Share Posted November 1, 2004 Lagrangian mechanics is fundamental to quantum field theory too. In fact, all of the modern high energy theories are described by Lagrangians (of more precisely, Lagrange densities). This is mainly because the Path Integral formalism of QFT weights each possible 'path' between initial and final conditions with the expenential of the action required for the path. The prefered path is then the one with the least action. Link to comment Share on other sites More sharing options...
pulkit Posted November 12, 2004 Author Share Posted November 12, 2004 Having studied Lagrangian mechnics somewhat by now, I must say I didn't understand the mathematical derivations used, but the methods of applications were mostly very mechanical and the differential equations obtained in the end did not seem humanly solvable. Link to comment Share on other sites More sharing options...
Perennial Posted November 12, 2004 Share Posted November 12, 2004 Does your "very mechanical" refer to what field of application you were studing or just that the applications were simplistic? Classical or quantum? I think they just look far worse than they actually are, the notation can do that sometimes. Link to comment Share on other sites More sharing options...
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